Flight Control Methods for Operating Close Formation Flight

This application is a divisional of co-pending U.S. patent application Ser. No. 15/075,098, filed Mar. 18, 2016. The entirety of which is herein incorporated by reference.

Embodiments of the present invention generally relate to methods and apparatus for close formation flight, and in particular for flight control for organizing and maintaining close formation flight. Non-limiting examples include providing sensing capabilities and flight control algorithms for maintaining relative aircraft positions within the formation that optimize flight performance.

Formation flight can be described as an arrangement of two or more aircraft flying together in a fixed pattern as a cohesive group. Different types of aircraft regularly can be flown in formation. One example of a formation flight is aerial refueling, where a receiver aircraft flies behind and below a tanker aircraft. In some of these formations, the aircraft are sufficiently close to one another that their wakes affect the aerodynamic characteristics of each other. This situation is sometimes referred to as “close formation flight”.

Close formation flight is attractive because of its potential to significantly reduce the aerodynamic drag and increase lift for the aircraft in formation. These effects in turn can lower power required for propulsion, reduce fuel consumption, and increase aircraft endurance, flight range, and payload.

While there are definite aerodynamic benefits of such formation flight, it has not been used in practice so far due to difficulties in flight control in close formation. Furthermore, the close proximity of the aircraft presents an unacceptably high risk of collision for most applications.

Close formation flight can be used for aerodynamic drag reduction, with a follower aircraft flying in the upwash generated by a leader aircraft. However, it has been very difficult for pilots on piloted aircraft and autopilots on unmanned airborne vehicles (UAV) to maintain proper positions in the formation for extended periods of time. In both cases, manned and unmanned aircraft, special automated control systems are required. Such systems must be able to determine relative locations of the aircraft and their trailing vortices to a very high degree of accuracy, in order to produce and sustain a close formation.

Wake turbulence is typically generated in the form of vortices trailing behind aircraft wing tips and other lifting surfaces. The pair of vortices generated by each aircraft is the result of lift being generated by the wings and air rotating around the wingtips from the high pressure regions at the bottom of the wing to the low pressure regions at the top of the wing.

Generally, these vortices are considered dangerous to other aircraft, particularly to those positioned directly behind within the wake turbulence. The wingtip vortices generated by a leading aircraft typically negatively affect the flight of trailing aircraft, by disrupting its aerodynamics, flight control capabilities and potentially damaging the aircraft or its cargo and injuring the crew. This makes manual flight control in close formation very difficult and challenging. As a result, conventional autopilot systems prevent close formation flight, by avoiding areas with wake turbulence.

Therefore, the inventors believe there is a need for an advanced adaptive flight control system with capabilities to provide reliable and accurate onboard flight control for aircraft in close formations. Such a system would enable multiple aircraft, both manned and unmanned, to produce and maintain close formation flight for extended time and thus achieve substantial benefits in aerodynamics performance outlined above.

Proposed solutions for such a system so far have been limited in their accuracy and efficacy. Some flight control systems are equipped to estimate the position of wingtip vortices trailing a leading aircraft, and control the flight characteristics of trailing aircraft to avoid the vortices. The position of a wingtip vortex relative to a trailing aircraft is estimated based on the flight characteristics of the leading aircraft and an estimate of the wind generated by the trailing aircraft.

Proposed close formation flight systems, as a rule, do not account for the effects of winds and drift on the wingtip vortices. The wingtip vortices, however, may move under the influence of winds and shift their position unpredictably between the leading and trailing aircraft. Because wingtip vortices cannot be directly visualized, the uncertainty in their position makes close formation flight not only challenging, but often impossible.

Older systems for formation flight control typically implemented a gradient peak-seeking approach to move the objects relative to each other to maximize or minimize a desired metric, i.e., fuel consumption. This approach uses a dither signal to determine a change in relative position to improve the metric. The change is effected, the results analyzed, and the position further updated once again using a dither signal to continually improve the metric. This gradient approach to peak-seeking may eventually position the aircraft close to the desired relative position in an ideal situation. However, such an approach is sluggish, time-consuming and unresponsive, so that in fast-changing conditions it becomes ineffective.

Some conventional formation flight control systems attempt to estimate the position of a wingtip vortex and control the position of a trailing aircraft relative to the estimated position. An inaccurate estimate of the vortex position leads to inaccurate relative positioning of the aircraft in formation. In addition, existing formation flight control systems fail to adequately account for vortex-induced aerodynamic effects acting on the aircraft.

Thus, the inventors have provided embodiments of improved apparatus, systems, and methods for close formation flight.

Embodiments of methods and apparatus for close formation flight are provided herein. In some embodiments, a method of operating aircraft for flight in close formation includes establishing a communication link between a first aircraft and a second aircraft, assigning to at least one of the first aircraft or the second aircraft, via the communication link, initial positions relative to one another in the close formation, providing flight control input for aligning the first and second aircraft in their respective initial positions, tracking, by at least one aircraft in the close formation, at least one vortex-generated by at least one other aircraft in the close formation, and based on the tracking, providing flight control input to adjust a relative position between the first aircraft and the second aircraft.

In some embodiments, a method of operating aircraft in a close formation flight includes determining relative positions between a first aircraft and a second aircraft, selecting, for each aircraft, a respective target position within the close formation and a corresponding boundary envelope encompassing each respective target position, and providing flight control input for aligning the first and second aircraft in respective initial positions within the close formation.

In some embodiments, a method of changing positions of at least two aircraft in a close formation flight includes determining new target positions of at least leader aircraft one follower aircraft, providing flight control input for course aligning the leader aircraft and the follower aircraft in respective initial positions within the close formation, tracking, by at least one aircraft in the close formation, at least one vortex generated by at least one other aircraft in the close formation, and based on the tracking, providing flight control input to adjust a relative position between the leader aircraft and the follower aircraft.

Other and further embodiments of the present invention are described below.

To facilitate understanding, identical reference numerals have been used, where possible, to designate identical elements that are common to the figures. The figures are not drawn to scale and may be simplified for clarity. It is contemplated that elements and features of one embodiment may be beneficially incorporated in other embodiments without further recitation.

In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of exemplary embodiments or other examples described herein. However, it will be understood that these embodiments and examples may be practiced without the specific details. In other instances, well-known methods, procedures, components, and/or circuits have not been described in detail, so as not to obscure the following description. Further, the embodiments disclosed are for exemplary purposes only and other embodiments may be employed in lieu of, or in combination with, the embodiments disclosed.

In accordance with embodiments of the present invention, methods and apparatus for producing and maintaining a close formation flight with multiple aircraft are provided. Aircraft in close formation typically fly together as a group in close proximity of each other and at the same air speed.shows for example an echelon formation, in which several fixed-wing aircraftmay be staggered behind each other. Many other formation patterns are possible:shows another example of a close formation, in which multiple aircraftform a V-pattern. The simplest close formationshown incan be produced by two aircraftand, in which the left wingtip of the leader aircraftand the follower aircraftare aligned behind each other along the streamwise direction. The defining characteristic of a close formation flight in the context of this invention is that the position of a follower aircraft should overlap with the streamwise projection of a leader aircraft. Thus, the two aircraft may be physically separated by a relatively large distance, they may still be considered in a close formation as long as this distance is shorter than the persistence length of a wingtip vortex (or the vortex decay distance) produced by the leader and this vortex can interact with the wingtip of the follower.

The alignment between aircraft in a close formation may be characterized by their tip-to-tip separation along the three axes (directions): X axis—the streamwise direction, Y axis—the spanwise direction and Z axis—the vertical direction.illustrates streamwise separation (distance) along the X axis.shows spanwise separationalong the Y axis between an aircraftand an aircraftin a dual formation. Similarly,shows vertical separationalong the Z axis between an aircraftand an aircraftin a dual formation. While the X distance in a close formation may be relatively large (ranging between 1 and 100 wingspans), the Y and Z distances should be relatively small, i.e., less than a single wing span or a fraction of a wingspan.

The tolerance to misalignment between aircraft in a close formation is determined by the characteristics of wingtip vortices. Different models have been used to describe and visualize these vortices.shows a horseshoe vortex modeltypically used to describe the wake behind a fixed-wing aircraft. In accordance with this model, planewith wingproduces a pair of vorticesoriginating from the wingtips. On the outside of vorticesthere are areas of upwash, whereas on the inside of vorticesthere is an area of downwash. Upwashmay reduce the drag and increase the lift of the follower aircraft. However, downwashmay do the opposite-reduce the lift and increase the drag. In this model we neglect the vortices produced by other surfaces on the aircraft, e.g., on the tail or fuselage. In addition, other more complex computer models may be used to describe vortices, such as for example a vortex lattice method, which may be more accurate than the horseshoe vortex model.

shows these vortices in a different view plane. Wingof aircraftproduces two wingtip vorticesand, where the right-hand vortex has a clockwise rotation and the left-hand vortex has a counterclockwise rotation. As result, the air on the outer side of the vortices has an upward velocity component (upwash) and the air on the inside of the vortices has a downward velocity component (downwash).

shows a vortex fieldhaving a single vortex in the Y-Z plane propagating along the X axis (flight direction). Particles in this vortex are subjected to circular motion around the vortex core at the center of the coordinate system of. For example, particlehas a tangential velocity V with corresponding Vand Vcomponents along the Y and Z axis, respectively.

If the vortex tangential velocity components Vand Vfor vortex(depicted in) are plotted in the reference frame of view planeof aircraft, their magnitudes (plotted on the vertical axes) would vary as functions of position in the Y-Z plane as shown in, respectively. For example,depicts a plotof the magnitude of vortex tangential velocity component V(on the vertical axis) as a function of position along the Z axis. Similarly,depicts a plotof the magnitude of vortex tangential velocity component V(on the vertical axis) as a function of position along the Y axis. Both components are close to zero near the vortex core (i.e., the vortex core center) and have opposite signs on opposite sides of the core. The vortex core position in this coordinate frame is approximately at y=1/2 (one-half of a wingspan) and z=0.

shows a dual aircraft close formationcomposed of two aircraftand. The leader aircraftgenerates vorticesand areas of upwashand downwash. In order to achieve the most beneficial formation flight configuration, aircraftshould maximize the overlap of its wing with the upwash areaand minimize the overlap with the downwash area. The aircraftandmay be of the same model type, but this need not be so. As such, the aircraftandmay have the same vortex, upwash and downwash generating characteristics, or they may be dissimilar with respect to any or all of those characteristics.

Similarly,shows a triple aircraft close formationcomposed of three aircraft,, and. Because the leader aircraftgenerates wingtip vorticesand upwash areason both sides of the wing, two follower aircraftandmay take aerodynamically beneficial positions behind the leader. In this case they may form a V-shaped close formation, in which the X distance between the leader and the followers is in the range of a fraction of a wingspan to few wingspans (less than 10). However, an extended close formation is possible too, where at least one of the follower aircraft is separated by an X distance of more than several wingspans (e.g., more than 10 and less than 100).

Larger close formation may comprise a greater number of aircraft, as shown in. Close formationis a V-formation, comprising at least 5 aircraft—,,,, andwith corresponding wake areas,,,, and(each wake area having corresponding upwash and downwash areas as discussed above). In this case, some aircraft may play the roles of both leaders and followers, e.g., aircraftand(both of which follow aircraft, and both of which lead other aircraft following them). The most beneficial position for each aircraft in this formation is also determined by the best overlap of the follower's wing area with the leader wake's upwash area. This typically implies a close tip-to-tip positioning in the Y-Z plane between any given leader-follower pair, i.e., a minimal separation in the Y and Z directions. The above description is valid for close formations in combination with different types of fixed wing aircraft, so that different types of aircraft may fly in the same formation and experience the same or similar aerodynamic benefits.

The wingtip vortices usually do not stay in the same place, and instead change their position as shown in formationin. In formation, the leader aircraftmay produce a pair of vortices, which subsequently will be subjected to interactions between themselves, interactions with other vortices, atmospheric turbulence, winds, drafts, and the like. As a result, vorticesmay experience a shift from their expected position by a walk-off distance, causing follower aircraftto miss the vortices and thus fail to produce a close formation. In addition, the size of the vortices may change too. The uncertainty in the vortex position and size may be reduced by reducing the X distance between the leader and the follower. However, this also significantly increases the risk of collision, reduces alignment tolerances between aircraft in the formation and makes formation flight control much more difficult.

Instead of estimating vortex positions from an indirect analysis of various data, a better approach is to sense the vortices directly and base formation flight control procedures on the real measurements of the vortex positions, rather than their estimates and predictions.

In accordance with embodiments of the present invention, a methodof vortex sensing (shown in) is provided in which the following may be implemented by the follower aircraft, either manually, automatically or both: measuring and collecting data atcharacterizing airflow near the aircraft, analyzing the collected data at, creating a computer model of a vortex field at, and evaluation of errors or differences between the model and the real vortex field at. These processes may be repeated until the value of error is below the acceptable limit or within the measurement uncertainty. The resulting model produces a set of static and dynamic parameters that simulate the airflow vector velocity field and its dynamic behavior. In general, the model may simulate difference airflow patterns and behaviors. In particular, it may simulate a single vortex, multiple vortices and vortex sheets. A simpler model (e.g., a single vortex model) may be less precise than a more complex (e.g., a vortex sheet model), but easier to process and faster to implement. As a result, a horseshoe vortex model shown inor even a simpler model of a single wingtip vortex may be well suited for the purposes of in-flight vortex sensing, simulation and analysis.

The computer vortex model may produce a vortex field similar to vortex fieldin. Instead of a complete vortex model, a simplified vortex model may be produced, in which only the vortex core and particularly its center position (an eye position) is characterized. The relative position of a vortex eye may be the primary parameter affecting the flight control during the close formation flight. In some situations, a complete or even partial vortex model may be difficult to produce due to insufficient or noisy airflow data. However, it is still may be possible to provide sufficient information about the relative vortex eye location, e.g., whether it is on the starboard or port side of the plane or whether it is above or below the plane.

Furthermore, additional processes may include one or more of varying Y and Z positions of the aircraft (either leader or follower), filtering and averaging airflow data provided by the measurements, using Kalman filters for data analysis and vortex model building, using complementary data to create and refine the vortex model (e.g., data provided by other aircraft in the same formation), and the like. Changing the aircraft position in the direction suggested by the vortex model may bring the aircraft closer to the vortex eye, improve data collection and analysis due to higher signal-to-noise ratio and improve the vortex model. Different vortex models may be used in different relative positions between the aircraft and the vortex, e.g., a simpler less accurate model may be used when the separation between the vortex core and the aircraft is relatively large (e.g., larger than half of a wingspan).

In accordance with embodiments of the present invention, a methodfor airflow vortex searching (shown in) is provided in which the following may be implemented by an aircraft (e.g., the follower aircraft), either manually, automatically or both: defining the target search area in XYZ space around the aircraft at, establishing a dithering flight pattern at, in which the aircraft may systematically fly through a grid of different X, Y, and Z coordinates, and continuous vortex sensing atuntil sufficient data is collected to create a robust vortex model. A robust vortex model may be defined as a model produced by a set of real-time measurements, in which at least some of its characteristic parameters (i.e., vortex core diameter, position, strength, etc.) have converged to stable values. A flight control system may specify the accuracy or precision required for vortex identification, which then would determine the time when the vortex search may be considered completed. For example, positional accuracy in the Y and Z directions may be specified as 5% of the wingspan. Additional processes may include one or more of communicating and exchanging telemetry data with other aircraft in the vicinity (particularly with the leader aircraft), using global positioning (GPS) data for narrowing the search area, using visual and other complimentary data for narrowing the search area, using neural network and deep learning algorithms for vortex patterns recognition, and the like. The search area in the method may be limited to the scan within a YZ coordinate plane at a fixed X position with respect to the leader aircraft.

In accordance with embodiments of the present invention, a methodof vortex tracking (shown in) is provided in which the following may be implemented by the follower aircraft, either manually, automatically or both: receiving continuously updated data of the airflow at, analyzing the airflow data at, mapping at least a part of the vortex field at, identifying the location of a vortex core at(particularly its center), and continuously or intermittently updating the position of the vortex core with respect to the aircraft at. Additional processes may include one or more of filtering and averaging airflow data provided by the measurements, using Kalman filters for data analysis and vortex model building, analysis and identification of the vortex core, using complementary data to create and refine the vortex model (e.g., data provided by other aircraft in the same formation), and the like.

In accordance with embodiments of the present invention, a method of multiple vortex tracking by an aircraft is provided in which the following may be implemented by the follower aircraft, either manually, automatically or both: receiving continuously updated data of the airflow around the aircraft (e.g., at) using onboard sensors, analyzing the received data creating computer vortex models (e.g., at), mapping the vortex field, subdividing the mapped vortex field into different vortex regions (e.g, at), identifying the location of respective vortex cores and particularly their centers, and continuously or intermittently updating the positions of the vortex cores with respect to the aircraft. Additional processes may include one or more of filtering and averaging airflow data provided by the measurements, using Kalman filters for data analysis and vortex model building, analysis and identification of the vortex cores, using neural network and deep learning algorithms for vortex pattern recognition, using complementary data to create and refine the vortex models (e.g., data provided by other aircraft in the same formation), and the like.

In accordance with embodiments of the present invention, a methodof vortex recovery (shown in) is provided in which the following may be implemented by the follower aircraft, either manually, automatically or both: preserving the computer model of the vortex field acquired by the aircraft at, initiating the vortex search at, reacquiring the vortex pattern at, and updating the computer model of the vortex and providing continuous updates for the vortex characteristics at. Additional processes may include one or more of using neural network processing and deep learning algorithms for vortex pattern recognition, using complementary data to create and refine the vortex models (e.g., data provided by other aircraft in the same formation), and the like.

In accordance with embodiments of the present invention, a methodof forming a close formation for a group flight between two aircraft (shown in) is provided in which the following may be implemented by the two aircraft, either manually, automatically or both: initial handshaking between the aircraft at, coarse aligning of their relative positions at, vortex searching and tracking at, and fine aligning of aircraft positions at. Additional processes may include one or more of establishing communication channel(s) and data exchange network(s) between the aircraft, choosing one or more formation flight metrics and evaluating its parameters, optimizing relative aircraft positions to maximize formation flight benefits by maximizing the metric parameters, and the like.

In accordance with embodiments of the present invention, a methodof forming a close formation for a group flight between more than two aircraft (shown in) is provided in which the following may be implemented by the aircraft, either manually, automatically or both: forming a two-aircraft formation at(as outlined above), selecting a formation pattern for additional aircraft at, adding at least one additional aircraft to the formation at the selected positions at. Optionally, at,may be repeated for any remaining aircraft at. Adding at least one additional aircraft to the formation (e.g., a first formation) at the selected positions may include adding one additional aircraft to the formation (e.g., the first formation) at the selected position, or adding another formation (e.g., a second formation) to the formation (e.g., the first formation) at the selected position. The latter scenario may include cases when a leader in the second formation becomes a follower in the first formation and vice versa.

In accordance with embodiments of the present invention, a method of adding an additional aircraft to an existing aircraft formation (similar to methodin) is provided in which the following may be implemented by the additional aircraft, either manually, automatically or both: establishing an initial handshake between aircraft in the existing formation and the additional aircraft, coarse aligning the position of the additional aircraft, vortex searching and tracking by the additional aircraft, and fine aligning of the additional aircraft with respect to other aircraft. Additional processes may include one or more of establishing communication channel(s) and data exchange network(s) between the aircraft, choosing formation flight metric and evaluating its parameters, optimizing relative aircraft positions to maximize formation flight benefits by maximizing the metric parameters, and the like.

In accordance with embodiments of the present invention, a methodof preliminary and initial handshaking between at least two aircraft (shown in) is provided in which the following may be implemented by the two aircraft, either manually, automatically or both: sending and receiving transponder signals by each aircraft at, establishing two-way communication links between aircraft at, and exchanging telemetry data at. The telemetry data may include information about such flight parameters as the position, airspeed, pitch angle, yaw angle, thrust, power consumption and acceleration of an aircraft, status and/or operating performance (e.g., power consumption) of on-board subsystems, such as propulsion systems, power systems, flight control systems, payload systems and other systems, data from various on-board sensors including airflow data near the aircraft and so on. Additional processes may include one or more of designating the roles of leaders and followers to specific aircraft at, selecting the pattern, shape and size for a formation at, configuring flight control systems for a formation flight at, and configuring payload for formation flight on at least one aircraft at. The same aircraft in a formation may undergo multiple handshaking steps. For example, it is possible for the same aircraft to be both a leader and a follower, in which case this aircraft may first go through the handshaking as a follower and subsequently as a leader aircraft do different handshaking with other aircraft (e.g., additional aircraft joining the formation).

In accordance with embodiments of the present invention, a method of networking between at least two aircraft is provided in which the following may be implemented by the two aircraft, either manually, automatically or both: establishing a communication network among the aircraft, exchanging telemetry data, and exchanging flight plans and commands. Additional processes may include one or more of selecting networking channel(s) and protocol(s), establishing a peer-to-peer network, establishing an ad-hoc network, establishing a network using radio frequency (RF) communication channels, establishing a network using free space optics, selecting and maintaining optimum distances between aircraft for reliable communication links, extending a network to elements outside of a formation (including other aircraft, ground-based network nodes (e.g., ground stations) and space-based network nodes (e.g., communication satellites)), and the like. The formation networking may be based on either mesh or point-to-point communication links. Different aircraft may play either different or similar roles in the network. In the former case, at least one aircraft may be a designated network controller, while in the latter case all aircraft equally share the tasks of managing network traffic.

In accordance with embodiments of the present invention, a methodof coarse alignment between two aircraft for a close formation flight (shown in) is provided in which the following may be implemented by the two aircraft, either manually, automatically or both: acquiring the current relative positions of the aircraft at, selecting target positions in the formation for each aircraft and their boundaries at, and adjusting coarse positions of each aircraft until they are within the target boundaries at. The target position may correspond to approximate expected or estimated position of a wingtip vortex behind a leader aircraft. Additional processes may include one or more of exchanging telemetry data between the aircraft, utilizing direct links between the aircraft (e.g., network links), utilizing indirect links between aircraft (e.g., via ground stations and satellites), using visual acquisition, recognition and analysis to obtain relative positioning data (e.g., using video cameras or thermal imaging), using beacon signals to facilitate coarse alignment, using triangulation to analyze data and calculate relative positions, and the like.

In accordance with embodiments of the present invention, a methodof fine aligning between two aircraft for a close formation flight (shown in) is provided in which the following may be implemented by the follower aircraft, either manually, automatically or both: vortex sensing at, evaluating the displacement of a vortex core with respect to the optimal position at, and changing the aircraft position at. The methodmay be repeated until the desired displacement is achieved (e.g., zero displacement or displacement within a predetermined tolerance of zero). Additional processes may include one or more of vortex searching, vortex tracking, evaluating the optimum position of the vortex core with respect to the aircraft, choosing a formation metric, evaluating and optimizing the metric, and the like. Changing the aircraft position atmay include changing the transverse, streamwise or X position, changing the lateral, spanwise or Y position, and changing the vertical or Z position of the follower aircraft with respect to the vortex core. Furthermore, a leader aircraft may facilitate the process of fine alignment between the leader and the follower by marking the approximate positions of its vortices, which in turn may be achieved by mechanical means (e.g., producing visual aids such as small particulates behind wingtips), electrical means (e.g., by ionizing air and emitting ionized gas at the wingtips), optical means (e.g., by emitting optical beams along the streamwise direction behind the wingtips), radio means (e.g. by emitting directional radio waves) and audio means (e.g., by emitting concentrated sound (or infra/ultra sound) waves along the streamwise direction behind the wingtips).

In accordance with embodiments of the present invention, a method of changing a formation flight pattern with at least one leader and one follower aircraft is provided in which the following may implemented by at least two aircraft: reassigning the roles of one former leader to become a follower and one former follower to become a leader, updating target positions for the respective aircraft, initiate position change in the formation by changing to coarse positions by the respective aircraft and perform fine aligning of the respective positions of each aircraft in the formation.

In accordance with embodiments of the present invention, a method of metric evaluation of a close formation is provided in which the following may be implemented by at least one follower aircraft, either manually, automatically or both: selecting an appropriate metric for evaluation of the flight formation (such as lift, drag, thrust, power consumption, fuel consumption, electrical consumption, electrical power supply current and voltage, angle of attack, rate of descent or ascent, air speed, rolling moment, yaw moment, pitching moment, vortex core displacement and others), collecting data for evaluating the metric, and calculating the metric using collected data. These processes may be used repeatedly and continuously during the formation flight to evaluate the conditions of a single pair formation (e.g., alignment between a leader and a follower) or of a larger formation with multiple leader-follower pairs. Additional processes may include one or more of measuring airflow characteristics around the follower aircraft, exchanging data (measured and calculated) between the aircraft, receiving additional data from other aircraft, analyzing collected data, using averaging and filtering for analyzing the data, using Kalman filters for data analysis and metric calculations, providing data used in calculations to other aircraft, providing the calculated metric to other aircraft in the formation, using several different metric parameters, switching between different metric parameters used for evaluation of the flight formation, and the like. Furthermore, in a formation with multiple followers a combined metric may be used to evaluate the formation as a whole, in which metric parameters from different followers are collected and analyzed, and a single figure of merit is produced to characterize the status of the formation as a whole. The combined formation flight metric may be the total propulsion power of an aircraft fleet in the formation, the total aerodynamic drag, the net fuel consumption of the fleet as a whole, the sum of quadrature deviations from the optimum relative vortex positions in the formation and others.

In accordance with embodiments of the present invention, a methodof close formation optimization (shown in) is provided in which the following may be implemented by at least one follower aircraft, either manually, automatically or both: providing the results of the metric evaluation at, changing flight parameters at, evaluating changes in the metric at, and providing feedback to flight control at, for example, to continue to change the flight parameters if the metric changes are positive and reversing the change if the metric changes are negative. The flight parameters that may be changed during the formation optimization include, but are not limited to: position, airspeed, pitch angle, roll angle, yaw angle, acceleration, thrust, power consumption, payload power consumption, and others. For example, the aircraft altitude may be continuously varied in a search of a minimum power consumption position in the vertical direction. Several flight parameters may be varied at the same time or sequentially. Additional processes may include one or more of providing flight parameter changes to other aircraft in the formation, coordinating flight parameter changes with actions of other aircraft (e.g., synchronizing or conversely alternating flight parameter scans between different aircraft), evaluating calculation errors and terminating the optimization process when effected changes are smaller than the calculated errors, and the like. For example, two follower aircraft in a formation may vary their positions synchronously without affecting each other evaluation of a formation flight metric corresponding to their respective leader-follower pairs. As a result, the combined formation flight metric may be evaluated and optimized faster than if they were varying their positions in sequence.

The methodmay also include using a deep learning computer algorithm for data processing and analysis during the formation flight optimization, which may recognize and record optimum follower aircraft positions with respect to either leader positions or vortex core positions in different flight conditions (i.e., flight speeds, altitudes, crosswinds, aircraft size, formation configuration, etc.). Once this position is learned, it can be quickly replicated with precision by the automatic flight control system after a particular vortex pattern is identified by the deep learning algorithm. As a result, the formation flight optimization can be dramatically faster.

In accordance with embodiments of the present invention, a method of maintaining a close formation is provided in which the following may be implemented by at least one follower aircraft, either manually, automatically or both: tracking a vortex produced by a leader aircraft, and adjusting the aircraft position with respect to the vortex core until the optimum vortex position is achieved. The optimum position may be defined in a number of ways, including but not limited to: a position of an aircraft relative to a vortex center or a leader aircraft that maximizes a given formation metric (e.g., maximizes the aerodynamic drag reduction), a position at which at which formation flight control inputs are zero (e.g., vortex eye sensor measurements are zero or close to zero as described below), a position predicted by a computer vortex model as being optimal for a given formation flight and so on. Of course, the optimum position can be reliably maintained only within the measurement uncertainties and accuracy of on-board sensors, and capabilities and precision of flight control systems. These processes may be repeated continuously or intermittently by one or more aircraft in the formation. Changes in the relative position of vortices may be induced by the motion of leader aircraft and atmospheric air movements. Continuous vortex tracking allows follower aircraft to maintain a persistent lock on the vortex position, to implement timely adjustments in the aircraft position and thus maintain an efficient close formation.